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GMAT Prep - Factor problem

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by Frankenstein » Tue Aug 09, 2011 9:42 pm
Hi,
450 = 2*3^2*5^2
Now, n^3 = 450*y = (2)(3^2)(5^2)y
As n and y are integers, y should be of the form (2^2)(3)(5)k^3 where k is an integer, so that
n^3 = (2^3)(3^3)(5^3)k^3 i.e. n = 2*3*5*k.
Now, y = (2^2)(3)(5)k^3
So, k^3 = y/(2^2)(3)(5)
So, y/(2^2)(3)(5) is always integer.
I -> k^3 ->definitely integer
II -> (k^3)(2/3) -> not necessarily an integer
III -> (k^3)(2/5) -> not necessarily an integer

Hence, B
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